How do you differentiate f(x)=(-e^x+secx)(3x^2-2x) using the product rule?

Dec 14, 2017

$f ' \left(x\right) = \left(- {e}^{x} + \sec x \tan x\right) \left(3 {x}^{2} - 2 x\right) + \left(- {e}^{x} + \sec x\right) \left(6 x - 2\right)$

Explanation:

$f \left(x\right) = \left(- {e}^{x} + \sec x\right) \left(3 {x}^{2} - 2 x\right) = g \left(x\right) h \left(x\right)$
$f ' \left(x\right) = g ' \left(x\right) h \left(x\right) + h ' \left(x\right) g \left(x\right)$

$g \left(x\right) = - {e}^{x} + \sec x$
$g ' \left(x\right) = - {e}^{x} + \sec x \tan x$

$h \left(x\right) = 3 {x}^{2} - 2 x$
$h ' \left(x\right) = 6 x - 2$

$f ' \left(x\right) = \left(- {e}^{x} + \sec x \tan x\right) \left(3 {x}^{2} - 2 x\right) + \left(- {e}^{x} + \sec x\right) \left(6 x - 2\right)$